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I meant if there exists some sequence which is non-convergent and we can make such subsequence from it which would be convergent. But from our discussion and my knowledge it is impossible to find such sequence, or am I wrong?

I have one more question. I am curious, where in practice are subsequences used, and how can I formally write that elements of my subsequence are for example every third element of my sequence?

Thanks guys, it is clear for me now. Mark44: All elements of second convergent subsequence are -1. Thanks for good example.

And I want to show if non-convergent sequence has always non-convergent subsequence.

I probably do not understand what is subsequence. Can you explain it in words and examples, please (not in formulas)?

Hi guys, I am not sure if my understanding of subsequence is right. For example I have sequence {x} from n=1 to infinity. Subsequence is when A) I chose for example every third term of that sequence so from sequence 1,2,3,4,5,6,7,... I choose subsequence 1,4,7...? B) Or subsequence is when I...

Thanks for answer.

Hi guys, I would like to ask if a set can contain coordinates of points, for example A={[1,3];[4,5];[4,7]} and if we can do Cartesian product of such sets, for example A={[1,3];[4,5]}, B={[7,8];[4,2]} A×B={[1,3][7,8];[1,3][4,2];[4,5][7,8];[4,5][4,2]} (is it correct to write it like that?). I am...